Note: I'm aware that after the psalms are read in certain services, we say "Glory to Thee our God and our Hope, glory to Thee." I'm just not familiar with the practices of added "our hope" or "Christ our God" to the opening prayer of the trisagion prayers.

"Glory to Thee, O Christ God and our Hope." occurs at the dismissal sequence for Vespers (when not part of a vigil), Matins(when separate from the Liturgy), and the Divine Liturgy. It never happens before the trisagion, or at other times except the dismissal. The addition of "and our hope" to the Glory to thee, our God, Glory to thee is incorrect, at least in the Russian practice. I have not seen this in the Greek horologia as well. Check the Antiochian liturgical books, but it will most likely not be there.